For $x$ units, revenue is $R(x) = 90x - 2x^{2}$ rupees and cost is $C(x) = 10x + 300$ rupees. What is the greatest profit?

₹20Correct answerYour answer₹499Correct answerYour answer₹500Correct answerYour answer₹800Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

Profit $P(x) = - 2 x^{2} + 80 x - 300$ , and $P'(x) = 80 - 4 x = 0$ at $x = 20$ ; $P'' < 0$ , a maximum.
The greatest profit is $P(20) = 500$ rupees.

Worth noting

₹800 forgets the fixed cost of ₹300.

Ten questions from Rate of Change, Marginal Cost & Revenue, at your own pace.

Ten questions from Rate of Change, Marginal Cost & Revenue, at your own pace.

For xxx units, revenue is R(x)=90x−2x2R(x) = 90x - 2x^{2}R(x)=90x−2x2 rupees and cost is C(x)=10x+300C(x) = 10x + 300C(x)=10x+300 rupees. What is the greatest profit?